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Study 50 Release
Study 50 reads raw CMS data from CERN in exact integers, seals each file it reads, and invites CERN and the CMS collaboration to validate its meaning.
Released with Affine IDE 0.2.6.1 Β· 2 October 2026
A Mac. The CMS detector's own raw bytes from the Large Hadron Collider in 2011, streamed from CERN's public Open Data portal. Real proton-proton collisions at 7 TeV, their pixel hits placed inside a drawing of CMS that turns in your hands. Exact integers throughout: no floating-point number touches the data.
That is Study 50 in the Affine IDE, a free native macOS app in Swift 6.4. No account, no GPU, nothing installed besides the IDE, nothing stored on disk except the integers the study finds.
One collision from 21 March 2011 (7,537 pixel hits, 77 tracks), drawn in the Affine IDE from the CMS RAW bytes. Cyan: pixel hits. Green: tracks, and their curves continued in the magnet. Outline after CMS's published dimensions, not to scale.
The IDE tells it as a documentary in seven chapters, from The bytes to The seal. The first collision of the first file is stamped 2011-03-21 03:09:05.121034 UTC in its event record, in bunch slot 2,705.
In the animation, gold bunches fly in along the beam and the detector answers from the inside out, ordered by radius for the eye (the pixel detector assigns every hit to one 25 ns bunch crossing). Each part glows by the bytes it sent: data volume, not energy. Pixel hits land where their chips sit, located by CMS's published cabling table (1,308 readout links, 15,865 chip entries), its chip-to-module map and layer radii of 4.4, 7.3 and 10.2 cm; in the first 460 collisions, 24 of 934,687 hits had no table entry. Placement is unaligned: barrel to about a millimetre, endcap about a centimetre.
The emerald tracks are aligned triplets, the pattern a charged particle leaves travelling out from the beam: one cluster per barrel layer, angle around the beam and distance along it growing in step with the radius. Each extends, dimmer, along a helix that continues its bend in CMS's 3.8 T field, drawn from unaligned clusters: an illustration of the path, not more hits and not a momentum. Extended back, the tracks gather on the beam line at the study's estimate of where the protons met.
Turn, slide and zoom the hologram; the form controls pick a chapter, step a collision or a file, or follow LIVE. The canvas shows the same collision three ways: from the side; down the beam, the three pixel rings seen along the beam pipe with every hit and track, out to the whole silicon tracker; and the LHC clock, one turn of the LHC as a ring of 3,564 bunch slots, the busy ones standing out, this collision's slot in gold and the pixel boards' slot marked when it differs. Beside it, two forms name every element on screen, with its colour and its value for this collision, and walk through the projection step by step as it plays.
One collision, the 2,700th in file 2: 2011-03-21 04:42:13.809764 UTC, luminosity section 910, event 488,465,760. It left 7,537 pixel hits, 1,964 clusters and 77 tracks, and 626 readout boards sent data (CMS numbers its boards in a space of 1,024 identifiers). Its tracks reach the beam line about 1 mm from the centre of CMS (z = β1 mm) in the study's unaligned geometry, where barrel placement holds to about a millimetre. Over the 276 of the first 460 collisions with more than 800 pixel hits, that point's median is β2 mm, with quartiles at β35 and +33 mm.
The LHC's bunch pattern, in the pixels. Across the five files sealed so far, 138 of the 3,564 bunch slots carry 93,110 of the 120,742 recorded events. At those slots an event lights up 2,850 pixels on average; at every other slot, 60. The busy slots are where the bunches collided.
A slot offset of exactly 3, in 3,854 events. In 3,854 of the 120,742 events, the bunch slot in the event record is exactly 3 lower than the slot in the pixel boards' headers. Where they differ, it is by 3, never any other amount. Its cause is not read at this level of the data: it is a question for CMS.
No CMS software, no ROOT library: Affine wrote its own decompressor and decoder, reading the raw-data formats from CMS's published CMSSW 5.3 sources. It streams each 2β3 GB file by HTTP byte range, keeps none of it, and checks every byte against CERN's published Adler-32: file 1's 2,175,229,386 bytes give 71522280, equal to CERN's. File 1's 16,915 recorded events carry 10,588,790 readout-board records (one per board per event), every header and trailer checked, none broken. One ECAL board flagged its own checksum and was counted; 145 pixel hits at addresses a chip does not have were refused by name.
Across the five files, an exact integer test (neighbouring pixels on one chip, row and column each within one) bonded 267,109,896 pixel hits into 69,339,194 clusters, and all 120,742 event records joined their detector readout.
Each file ends in two SHA-256 seals, over its census and index. File 1's census seal, fb007f85c22e10e676cca1ce60e21915989423a066f6e02d0a64a20dac56a19a, reproduced byte for byte on a re-run, so far on one Mac; anyone who runs Study 50 reads the same bytes and must reach the same seals. The IDE's prover: 337 of 337 checks hold, 0 floating-point sites in the study's law.
Module orientation is not in the raw data, so Affine kept the one under which the most tracks agree on one collision point. On collisions held out of that choice, tracks agreeing within 3 mm rose from 165 of 862 to 402 of 1,815. CMS can check the choice against its own geometry.
Next tier: momenta, masses and particle identities, which need CMS's alignment and calibration (global tag FT_53_LV5_AN1) and reconstruction beyond the pixel layers, under the same exact-integer law.
What we offer. The Study 50 law is open to CERN and the CMS collaboration for study: the Swift source of the decoder, placement, bonding and track tests, with the transcripts, seals and per-collision indexes, which locate each collision's bytes in CERN's file.
How to validate it. CMS's reconstruction of these events is public as CERN Open Data record 24; the code to repeat it is record 463. Match collisions on (run, luminosity section, event) and compare:
- Affine's collision point along the beam against CMS's reconstructed primary vertices.
- Affine's three-layer barrel tracks against CMS's tracks in the same part of the detector.
- The -3 slot offset: tell us what it is.
"Study 50 reads CMS's raw bytes exactly and seals what it finds. We are opening the law, its transcripts, seals and indexes to CERN and the CMS collaboration: we will allow them to study it and validate its meaning."
β the founder of Affine.Earth
Free in Affine IDE 0.2.6.1 for macOS: affine.earth/download.
Affine.Earth is an exact-integer substrate. Every verdict is computed in integers and sealed, so it is the same on every machine. The Affine IDE is its native Mac client. affine.earth
CERN Open Data record 35, /MinimumBias/Run2011A-v1/RAW, DOI 10.7483/OPENDATA.CMS.I8HN.DF32, license CC0. The CMS detector at the LHC recorded it in run 160957 in 2011: proton-proton collisions at 7 TeV (3.5 TeV per beam). The record describes them as soft-QCD events, selected for the presence of low-energy particles. The dataset is named MinimumBias: these are the LHC's ordinary collisions. The study's manifest covers 71 files and 248,789,344,017 bytes, and the record lists 1,913,190 recorded events. Neither CERN nor the CMS collaboration has endorsed or reviewed this work. Study 50 is Affine's own work, and this release is an invitation to CERN and the CMS collaboration, not a partnership.